DUP deputy leader Nigel Dodds has said Brexit negotiations have become a "battle for the union itself" as the European Union and British government appear no closer to agreeing a deal.
Mr Dodds said the party was not prepared to move on its red line of the north leaving the EU single market along with the rest of the United Kingdom. He warned the EU's continued push fo ra backstop would "inevitably lead to a stand off".
Speaking to the BBC this morning, the North Belfast MP called on the British government to deliver on Brexit promises.
"The Conservative Party are deeply troubled about the way things are going," he said. "What we need to see is a policy that delivers Brexit and which safeguards the union.
"Mrs May said that there would be no new borders within the United Kingdom, the whole of the UK including Northern Ireland would leave the Customs Union and the Single Market.
"What we need to see is that delivered. We want to see a sensible Brexit which delivers on the promises, because the whole of the United Kingdom voted that way."
Mr Dodds denied that the DUP want to see a no-deal Brexit.
"We don't want a no-deal, but if the arrogance and hubris of the EU continues, with Michel Barnier putting forward proposals about breaking up the Union, if they continue to maintain that hard line then the chance of a no-deal does increase," he said.
The Brexit talks have run into a "significant problem" over the fraught issue of the border, British government sources have said.
Negotiations are on a knife-edge after a hastily-arranged meeting on Sunday between EU chief negotiator Michel Barnier and Britain's Brexit secretary Dominic Raab broke up without a breakthrough.
Discussions were said to have broken down after EU negotiators demanded a "backstop to the backstop" to prevent a return of a "hard border" between Northern Ireland and the Republic.
Theresa May has proposed the backstop - which would effectively keep Northern Ireland in the single market while a permanent solution is found - should apply to the whole of the UK.
However it is understood the EU is insisting it should be backed up by the original Northern Ireland-only backstop as it first proposed.
That could lead to customs checks on goods travelling between Northern Ireland and the rest of the UK - effectively imposing a "border in the Irish Sea" - something Mrs May has said is unacceptable.
The impasse threatens to throw into disarray carefully choreographed plans which would have seen EU leaders meeting in Brussels on Wednesday give the green light to a special summit in November to finalise the terms of the UK's withdrawal from the bloc.
DUP leader Arlene Foster is meeting Leo Varadkar for a private dinner in Dublin this evening.
It is understood she will stress a desire for a strong relationship between Northern Ireland and the Republic of Ireland to continue post-Brexit.
She will tell Mr Varadkar that she wants to see a deal that works for both jurisdictions.
It is understood Mrs Foster will seek to strike a conciliatory tone with Mr Varadkar after a year that has seen relations between the pair fray over Brexit.
On her visit to Dublin, Mrs Foster will also meet Micheál Martin, the leader of main opposition party Fianna Fáil.
She also will meet a leading cardiologist to discuss a cross-border heart service that treats children from both sides of the border and visit St Patrick's Church of Ireland cathedral.
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Following Sunday's meeting in Brussels, Mr Barnier said that, despite "intense efforts", there had been a failure to reach agreement on the border issue.
The British government said there were still "unresolved issues" relating to the backstop but that it remained committed to making progress at the European Council meeting.
But with Mrs May under siege from Tory Eurosceptics and her DUP parliamentary allies, her room for manoeuvre is severely restricted.
Tánaiste Simon Coveney said it was "frustrating and disappointing" that negotiators had "disengaged" but insisted that the temporary border backstop wanted by the UK was a non-starter.
Arriving in Brussels he said that Dublin and the EU simply wanted Theresa May to follow through with agreements already made in March and December.
He said: "A backstop can't be time-limited.
"That is new, it hasn't been there before. Nobody was suggesting in March that a backstop would be time-limited in terms of picking a date in the future as an endpoint for the backstop.
"The backstop will be there unless and until something else is agreed, but unless you have something to replace it well then the backstop needs to be there as an insurance mechanism.
"That is all we are asking for, that's all the Michel Barnier taskforce is also looking for now in terms of legal text."
Writing in the Daily Telegraph, the DUP's Westminster leader, Nigel Dodds, said: "One part of the UK cannot be left behind, bound to rules set in Brussels. The constitutional and economic consequences of such an approach would be catastrophic in the long run."
For Labour, Sir Keir Starmer said the British government must now publish details of its revised proposals for the Irish border.
"At the moment we don't even know what the proposal is that everybody has fallen out about over the weekend," the shadow Brexit secretary told BBC Radio 4's Today programme.
"That needs to be looked at and scrutinised in Parliament."
The Republic's ambassador to the UK, Adrian O'Neill, said events in Brussels were a "setback" and could increase the prospect of a no-deal Brexit.
He told BBC Radio 4's Westminster Hour: "Time is running out, there is no doubt about that. In all member states, preparation for all eventualities are ramping up quite significantly."
The special EU summit pencilled in for November to sign off a Brexit agreement could instead end up being used as an emergency meeting to discuss "no-deal" plans.
Mrs May is set to meet Sinn Féin leader Mary Lou McDonald in Westminster today.
The febrile atmosphere in the Tory ranks has seen former Brexit secretary David Davis emerge as a potential successor to Mrs May.
Tory MP Nadine Dorries publicly suggested he could be the leader to deliver the kind of Brexit sought by Eurosceptics.
The prime minister's critics believe the threshold of 48 Tory MPs calling for a no-confidence vote could be passed by Wednesday, depending on events in Brussels.
Allies of Mr Davis said he has been contacted by several Tory MPs urging him to run for the leadership and he is understood to be prepared to take part in a contest.
Ms Dorries backed Mr Davis for the top job, saying: "Getting May out and him becoming an interim leader may be the only way to deliver Brexit and FTA (a free-trade agreement)."
